Description

where σ̂eσ^e is an independent estimate of the standard error of the xixi's. The most common use of this statistic is in the testing of means from a balanced design. In this case for a set of group means, T1,T2, … ,TrT-1,T-2,…,T-r, the Studentized range statistic is defined to be the difference between the largest and smallest means, TlargestT-largest and TsmallestT-smallest, divided by the square root of the mean-square experimental error, MSerrorMSerror, over the number of observations in each group, nn, i.e.,

q = (Tlargest − Tsmallest)/(sqrt(MSerror / n)).

q=T-largest-T-smallestMSerror/n.

The Studentized range statistic can be used as part of a multiple comparisons procedure such as the Newman–Keuls procedure or Duncan's multiple range test (see Montgomery (1984) and Winer (1970)).

For a Studentized range statistic the probability integral, P(q ; v,r)P(q;v,r), for vv degrees of freedom and rr groups can be written as:

Accuracy

The returned value will have absolute accuracy to at least four decimal places (usually five), unless ifail = 2ifail=2. When ifail = 2ifail=2 it is usual that the returned value will be a good estimate of the true value.